Association Rule Mining

Objective: As a Data Scientist at FDMart Grocery after analyzing FDMart transaction database to identify interesting patterns from the database.

Overview: The dataset provided by FDMart grocery has 106 items that are on sale and total of 64808 transactions. The most frequent item found in the grocery shop is fresh vegetables which is present in 30% of the total transaction available in the dataset. Second most frequent items are fresh fruit and some of the equally frequent items are cheese, soup and dried fruits etc. The following graph reflects the that FDMart customers buy fresh items and healthy food like cheese dried fruit, juices more frequently as compare to bottled or canned items.

# Load package arules
library(arules)
library(arulesViz)
library(grid)
# List datasets in package
#data()
#load dataset 
transactions <- read.transactions("transactions.txt",format="single",sep=",",cols=c(1,2))

class(transactions)

[1] "transactions"
attr(,"package")
[1] "arules"

# summary showing basic statistics of the data set
summary(transactions)

transactions as itemMatrix in sparse format with
 64809 rows (elements/itemsets/transactions) and
 107 columns (items) and a density of 0.05353055 

most frequent items:
Fresh Vegetables      Fresh Fruit           Cheese             Soup      Dried Fruit          (Other) 
           20001            12641             9380             8209             8140           312840 

element (itemset/transaction) length distribution:
sizes
    1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17 
 4490  8628  8522 10010  8344  9013  6075  2247   997  1024   999   672   436   249   235   226   149 
   18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33    34 
   96    80    94    91    77    85    91    92   123   162   207   226   216   174   152   124   115 
   35    36    37    38    39    40    41    42    43    44 
   79    63    62    28    26    14     8     6     1     1 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   3.000   5.000   5.728   6.000  44.000 

includes extended item information - examples:
        labels
1 Acetominifen
2    Anchovies
3      Aspirin

includes extended transaction information - examples:
  transactionID
1             1
2            10
3           100

# plot frequencies of frequent items in the dataset
itemFrequencyPlot(transactions, support=0.1, cex.names=0.8)

Item frequency plot-With a ( minimum support .01 and .2 confidence )

On an average, each itemset or basket contains 5 to 6 items. In other words, basket having less than 5 items is more frequent as compare to baskets having more than 15 items. Buyers generally comes to purchase fewer items from the shop. Support being set to .01 means that plot only includes item set having more than 1 repetition in each 100 transactions. Anything less than that is ignored for the study. Support shows the frequency of the patterns in the rule; it is the percentage of transactions that contain both A and B, i.e. Support = Probability (A and B) Support = (# of transactions involving A and B) / (total number of transactions).

Confidence is the strength of implication of a rule; it is the percentage of transactions that contain B if they contain A, i.e. Confidence = Probability (B if A) = P(B/A) Confidence = (# of transactions involving A and B) / (total number of transactions that have A).

Correlation analysis The lift score . Lift = 1 ??? A and B are independent . Lift > 1 ??? A and B are positively correlated . Lift < 1 ??? A and B are negatively correlated Running the association rule mining with Apriori algorithm ( support=0.01,confidence=0.2) resulted in 9224 rules with a mean of 3.484 items in an item set and maximum of 5 items , item set . Plot of all 9224 rule (support= 0.01, confidence= 0.2)

# Mine association rules using Apriori algorithm implemented in arules.
rules <- apriori(transactions, parameter = list(support= 0.01 , confidence= 0.2))

summary of rules:

#summary of rules
summary(rules)

inspect top 5 rules by highest lift

# Inspect rules
#inspect(rules)
#inspect top 5 rules by highest lift
inspect(head(sort(rules, by ="lift"),5))

Above given item set are picked from the plot that reflects some very strong correlation between items like cooking oil ,rice and pots and pan(lift=28.18). Other than that chips ,deodorizer ,pancake mix and frozen chicken has a strong correlation with shrimp. I other words, people who buy cooking oil and rice are 75 % likely to buy pots and pans . Also buyers who buy chips and pancake mix are 75 % likely to buy shrimp. These rules and their subset provide some very interesting patterns discussed in the next section.

# Visualization of rules
#Plotting rules
plot(rules)

# Interactive plots for rules
sel <- plot(rules, measure=c("support", "lift"), shading="confidence", interactive=FALSE)

# Two key plot
plot(rules , shading="order", control=list(main="two-key plot"))

# 1.Purchase pattern related to beverages (Wine , Beer )
#Find subset of rules that has Wine on the right hand side
RulesBev1 <- subset(rules, subset = rhs %ain% "Wine")
summary(RulesBev1)

set of 16 rules

rule length distribution (lhs + rhs):sizes
2 3 
9 7 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   2.000   2.000   2.438   3.000   3.000 

summary of quality measures:
    support          confidence          lift      
 Min.   :0.01015   Min.   :0.2081   Min.   :2.032  
 1st Qu.:0.01030   1st Qu.:0.2407   1st Qu.:2.349  
 Median :0.01150   Median :0.2982   Median :2.910  
 Mean   :0.01228   Mean   :0.3740   Mean   :3.650  
 3rd Qu.:0.01330   3rd Qu.:0.4790   3rd Qu.:4.675  
 Max.   :0.01719   Max.   :0.6748   Max.   :6.586  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

inspect(RulesBev1)

     lhs                                 rhs    support    confidence lift    
[1]  {Spices}                         => {Wine} 0.01015291 0.2222973  2.169709
[2]  {Candles}                        => {Wine} 0.01181935 0.4633999  4.522964
[3]  {Fresh Chicken}                  => {Wine} 0.01155704 0.4434577  4.328320
[4]  {Sauces}                         => {Wine} 0.01641747 0.5256917  5.130957
[5]  {Crackers}                       => {Wine} 0.01144903 0.2620982  2.558181
[6]  {Gum}                            => {Wine} 0.01078554 0.2676110  2.611988
[7]  {Sponges}                        => {Wine} 0.01038436 0.2836072  2.768118
[8]  {Cooking Oil}                    => {Wine} 0.01718897 0.2388508  2.331277
[9]  {Rice}                           => {Wine} 0.01276057 0.2139715  2.088446
[10] {Candles,Fresh Vegetables}       => {Wine} 0.01029178 0.6233645  6.084281
[11] {Fresh Chicken,Fresh Vegetables} => {Wine} 0.01023006 0.6356663  6.204352
[12] {Fresh Vegetables,Sauces}        => {Wine} 0.01492077 0.6748081  6.586391
[13] {Cooking Oil,Fresh Vegetables}   => {Wine} 0.01272971 0.3668297  3.580402
[14] {Fresh Vegetables,Rice}          => {Wine} 0.01030721 0.3127341  3.052407
[15] {Fresh Vegetables,Juice}         => {Wine} 0.01024549 0.2412791  2.354978
[16] {Fresh Fruit,Fresh Vegetables}   => {Wine} 0.01530652 0.2081410  2.031538

#Plotting RulesBev1
plot(RulesBev1, method="matrix", measure="lift", control=list(reorder=TRUE))

Itemsets in Antecedent (LHS)
 [1] "{Fresh Fruit,Fresh Vegetables}"   "{Rice}"                          
 [3] "{Spices}"                         "{Cooking Oil}"                   
 [5] "{Fresh Vegetables,Juice}"         "{Crackers}"                      
 [7] "{Gum}"                            "{Sponges}"                       
 [9] "{Fresh Vegetables,Rice}"          "{Cooking Oil,Fresh Vegetables}"  
[11] "{Fresh Chicken}"                  "{Candles}"                       
[13] "{Sauces}"                         "{Candles,Fresh Vegetables}"      
[15] "{Fresh Chicken,Fresh Vegetables}" "{Fresh Vegetables,Sauces}"       
Itemsets in Consequent (RHS)
[1] "{Wine}"

Market Basket Analysis: 1.) Purchase patterns related to beverages (Wine, Beer etc.)

a.) In the matrix plot with antecedents and consequents based on 16 rules ,we found that with fresh items like fresh vegetables, candles ,sauces, deodorizer ,wine is found to be most consequent item.

b.) Mining the rules for Wine on the rhs, resulted that there is hardly any correlation between wine and Beer . Out of 16 rules, results reflected wine on the RHS but not a single item set with Beer on the lhs. In other words people who are buying Beer rarely buy Wine. Wine is combined with items like sauces ,fresh vegetables and candles. Moreover, people who eat healthy fresh food like fresh chicken and fresh vegetable are more likely to buy wine. These buyers are mostly who cook food on daily basis

#Find subset of rules that has Wine and Beer in the left hand side.
RulesBev2 <- subset(rules, subset = lhs %ain%  "Wine"|lhs %ain%  "Beer" )
summary(RulesBev2)

set of 36 rules

rule length distribution (lhs + rhs):sizes
 2  3 
22 14 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   2.000   2.000   2.389   3.000   3.000 

summary of quality measures:
    support          confidence          lift       
 Min.   :0.01023   Min.   :0.2033   Min.   : 1.170  
 1st Qu.:0.01037   1st Qu.:0.2568   1st Qu.: 2.355  
 Median :0.01285   Median :0.2778   Median : 2.930  
 Mean   :0.01389   Mean   :0.3766   Mean   : 3.663  
 3rd Qu.:0.01492   3rd Qu.:0.3765   3rd Qu.: 4.110  
 Max.   :0.03989   Max.   :0.9088   Max.   :11.978  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

inspect(RulesBev2)

     lhs                        rhs                 support    confidence lift     
[1]  {Beer}                  => {Gum}               0.01370180 0.2723091   6.756539
[2]  {Beer}                  => {Sour Cream}        0.01100156 0.2186446   4.609674
[3]  {Beer}                  => {Pizza}             0.01023006 0.2033119   2.373705
[4]  {Beer}                  => {Deodorizers}       0.01293030 0.2569764   6.200440
[5]  {Beer}                  => {Cottage Cheese}    0.01038436 0.2063784   3.723602
[6]  {Beer}                  => {Jam}               0.01104785 0.2195646   3.256238
[7]  {Beer}                  => {Jelly}             0.01083183 0.2152714   3.000973
[8]  {Beer}                  => {Frozen Chicken}    0.01365551 0.2713891   4.035902
[9]  {Beer}                  => {Chips}             0.01607801 0.3195339   3.304399
[10] {Beer}                  => {Eggs}              0.01433443 0.2848819   3.144229
[11] {Beer}                  => {Pancake Mix}       0.01277600 0.2539098   4.709686
[12] {Beer}                  => {Waffles}           0.01404126 0.2790555   3.402692
[13] {Beer}                  => {Paper Wipes}       0.01181935 0.2348973   2.132137
[14] {Beer}                  => {Canned Vegetables} 0.01530652 0.3042012   2.915554
[15] {Beer}                  => {Cereal}            0.01382524 0.2747623   3.068069
[16] {Beer}                  => {Sliced Bread}      0.01399497 0.2781355   2.655914
[17] {Beer}                  => {Juice}             0.01396411 0.2775222   2.540746
[18] {Beer}                  => {Cheese}            0.01533738 0.3048145   2.106047
[19] {Beer}                  => {Fresh Fruit}       0.01237482 0.2459368   1.260891
[20] {Beer}                  => {Fresh Vegetables}  0.01816106 0.3609322   1.169524
[21] {Wine}                  => {Fresh Fruit}       0.02632350 0.2569277   1.317240
[22] {Wine}                  => {Fresh Vegetables}  0.03988644 0.3893072   1.261468
[23] {Candles,Wine}          => {Fresh Vegetables}  0.01029178 0.8707572   2.821504
[24] {Fresh Vegetables,Wine} => {Candles}           0.01029178 0.2580271  10.116441
[25] {Fresh Chicken,Wine}    => {Fresh Vegetables}  0.01023006 0.8851802   2.868239
[26] {Fresh Vegetables,Wine} => {Fresh Chicken}     0.01023006 0.2564797   9.841440
[27] {Sauces,Wine}           => {Fresh Vegetables}  0.01492077 0.9088346   2.944886
[28] {Fresh Vegetables,Wine} => {Sauces}            0.01492077 0.3740812  11.978177
[29] {Cooking Oil,Wine}      => {Fresh Vegetables}  0.01272971 0.7405745   2.399675
[30] {Fresh Vegetables,Wine} => {Cooking Oil}       0.01272971 0.3191489   4.434761
[31] {Rice,Wine}             => {Fresh Vegetables}  0.01030721 0.8077388   2.617306
[32] {Fresh Vegetables,Wine} => {Rice}              0.01030721 0.2584139   4.333130
[33] {Juice,Wine}            => {Fresh Vegetables}  0.01024549 0.7272727   2.356573
[34] {Fresh Vegetables,Wine} => {Juice}             0.01024549 0.2568665   2.351641
[35] {Fresh Fruit,Wine}      => {Fresh Vegetables}  0.01530652 0.5814771   1.884153
[36] {Fresh Vegetables,Wine} => {Fresh Fruit}       0.01530652 0.3837524   1.967456

c.) Further creating sub rules to get wine and Beer on the lhs we got 36 rules in which most baskets were with 2 or 3 items in it. Beer and wine were not present in a single item set. Note: Beer is mostly purchase with gums, pizza , frozen food items, eggs and chips where as wine is frequently purchased with fresh vegetables, fresh chicken and candles. But these two items are not found together in any of the item set.

#generating rules for beer on RHS from transactional data using apriori algorithm
beerRule<-apriori(data=transactions, parameter=list(supp=0.01,conf = 0.15,minlen=2), 
                  appearance = list(default="lhs",rhs="Beer"),
                  control = list(verbose=F))
#Sorting Beerrule by confidence in descending order
rules1<-sort(beerRule, decreasing=TRUE,by="confidence")
summary(rules1)

set of 13 rules

rule length distribution (lhs + rhs):sizes
 2 
13 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      2       2       2       2       2       2 

summary of quality measures:
    support          confidence          lift      
 Min.   :0.01006   Min.   :0.1510   Min.   :3.001  
 1st Qu.:0.01100   1st Qu.:0.1638   1st Qu.:3.256  
 Median :0.01293   Median :0.1712   Median :3.403  
 Mean   :0.01267   Mean   :0.2035   Mean   :4.043  
 3rd Qu.:0.01383   3rd Qu.:0.2319   3rd Qu.:4.610  
 Max.   :0.01608   Max.   :0.3400   Max.   :6.757  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01       0.15

inspect(rules1)

     lhs                 rhs    support    confidence lift    
[1]  {Gum}            => {Beer} 0.01370180 0.3399694  6.756539
[2]  {Deodorizers}    => {Beer} 0.01293030 0.3119881  6.200440
[3]  {Pancake Mix}    => {Beer} 0.01277600 0.2369777  4.709686
[4]  {Sour Cream}     => {Beer} 0.01100156 0.2319453  4.609674
[5]  {Frozen Chicken} => {Beer} 0.01365551 0.2030748  4.035902
[6]  {Cottage Cheese} => {Beer} 0.01038436 0.1873608  3.723602
[7]  {Waffles}        => {Beer} 0.01404126 0.1712135  3.402692
[8]  {Rice}           => {Beer} 0.01006033 0.1686934  3.352607
[9]  {Chips}          => {Beer} 0.01607801 0.1662678  3.304399
[10] {Jam}            => {Beer} 0.01104785 0.1638444  3.256238
[11] {Eggs}           => {Beer} 0.01433443 0.1582084  3.144229
[12] {Cereal}         => {Beer} 0.01382524 0.1543763  3.068069
[13] {Jelly}          => {Beer} 0.01083183 0.1510002  3.000973

Some Visualization for above subrules

# Visualization for 1st question subrules
# plot for subrules
plot(RulesBev1,method="graph",interactive=FALSE,shading=NA)

plot(RulesBev2,method="graph",interactive=FALSE,shading=NA)

plot(beerRule,method="graph",interactive=FALSE,shading=NA)

When finding a rule for wine or beer on the left hand side (means finding basket in which people who buy wine or beer are most likely to buy what other items).The search resulted in wine and beer separately on the lhs of the item set which depicts that wine and beer doesn’t go together. Results/Findings: 1.) Wine and Beer has no correlation. These two items very rarely go together. 2.) Beer is mostly purchase with gums, pizza , frozen food items, eggs and chips where as wine is frequently purchased with fresh vegetables, fresh chicken and candles .People buy it with items used for making dinner and full meals. 3.) There is positive relation between candles and wine too. The person who buy candles are 62% likely to buy wine from that store. 4.) Beer is purchased mostly in small baskets where there is 2 or less items in a basket.

# 2.Pattern with respect to canned Vs fresh
#Subrules for Fresh Vegetables on the rhs
FreshRules <- subset(rules, subset = rhs %pin% "Fresh Vegetables")
summary(FreshRules)

set of 864 rules

rule length distribution (lhs + rhs):sizes
  1   2   3   4   5 
  1  74 296 460  33 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   3.000   4.000   3.521   4.000   5.000 

summary of quality measures:
    support          confidence          lift       
 Min.   :0.01001   Min.   :0.2198   Min.   :0.7122  
 1st Qu.:0.01102   1st Qu.:0.6880   1st Qu.:2.2292  
 Median :0.01129   Median :0.8294   Median :2.6874  
 Mean   :0.01323   Mean   :0.7751   Mean   :2.5116  
 3rd Qu.:0.01269   3rd Qu.:0.9089   3rd Qu.:2.9450  
 Max.   :0.30861   Max.   :0.9742   Max.   :3.1566  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

inspect(FreshRules[1:20])

     lhs                    rhs                support    confidence lift     
[1]  {}                  => {Fresh Vegetables} 0.30861454 0.3086145  1.0000000
[2]  {Canned Fruit}      => {Fresh Vegetables} 0.01418013 0.4240886  1.3741692
[3]  {Deli Salads}       => {Fresh Vegetables} 0.01220509 0.2878457  0.9327030
[4]  {Personal Hygiene}  => {Fresh Vegetables} 0.01692666 0.3269747  1.0594921
[5]  {Plastic Utensils}  => {Fresh Vegetables} 0.01127930 0.2515485  0.8150896
[6]  {Spices}            => {Fresh Vegetables} 0.01904057 0.4168919  1.3508498
[7]  {Popcorn}           => {Fresh Vegetables} 0.01089355 0.2406271  0.7797012
[8]  {Aspirin}           => {Fresh Vegetables} 0.01185021 0.3221477  1.0438512
[9]  {Candles}           => {Fresh Vegetables} 0.01651005 0.6473079  2.0974641
[10] {Fresh Chicken}     => {Fresh Vegetables} 0.01609344 0.6175252  2.0009594
[11] {Pots and Pans}     => {Fresh Vegetables} 0.01660263 0.6237681  2.0211883
[12] {Tofu}              => {Fresh Vegetables} 0.01154161 0.5006693  1.6223129
[13] {Fashion Magazines} => {Fresh Vegetables} 0.01274514 0.5481088  1.7760304
[14] {Popsicles}         => {Fresh Vegetables} 0.01555340 0.2593927  0.8405070
[15] {Hard Candy}        => {Fresh Vegetables} 0.01538367 0.4253413  1.3782283
[16] {Sauces}            => {Fresh Vegetables} 0.02211113 0.7080040  2.2941367
[17] {Oysters}           => {Fresh Vegetables} 0.01018377 0.4153556  1.3458717
[18] {Dips}              => {Fresh Vegetables} 0.01606258 0.2440225  0.7907032
[19] {Sugar}             => {Fresh Vegetables} 0.01968862 0.5085692  1.6479105
[20] {Tools}             => {Fresh Vegetables} 0.01612430 0.4477292  1.4507716

2.) Canned vs Fresh a.) Another very important category to item is canned and fresh food. Which has mainly fresh vegetables ,fresh fruits ,canned vegetables and canned fruits. Looking for more item sets having baskets with fresh vegetables and fresh fruits, we found with 864 item sets having fresh vegetables and 133 itemset with fresh fruits on the right hand side of the itemset .

# Subrules for Fresh Fruit on the rhs
FreshRules1 <- subset(rules, subset = rhs %pin% "Fresh Fruit")
summary(FreshRules1)

set of 133 rules

rule length distribution (lhs + rhs):sizes
 2  3  4 
49 83  1 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   2.000   3.000   2.639   3.000   4.000 

summary of quality measures:
    support          confidence          lift      
 Min.   :0.01003   Min.   :0.2009   Min.   :1.030  
 1st Qu.:0.01086   1st Qu.:0.3236   1st Qu.:1.659  
 Median :0.01202   Median :0.4008   Median :2.055  
 Mean   :0.01463   Mean   :0.4431   Mean   :2.272  
 3rd Qu.:0.01629   3rd Qu.:0.5385   3rd Qu.:2.761  
 Max.   :0.07354   Max.   :0.8639   Max.   :4.429  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

inspect(FreshRules1[1:20])

     lhs                    rhs           support    confidence lift    
[1]  {Spices}            => {Fresh Fruit} 0.01405669 0.3077703  1.577904
[2]  {Candles}           => {Fresh Fruit} 0.01245197 0.4882033  2.502964
[3]  {Fresh Chicken}     => {Fresh Fruit} 0.01265256 0.4854944  2.489076
[4]  {Fashion Magazines} => {Fresh Fruit} 0.01016834 0.4372926  2.241951
[5]  {Hard Candy}        => {Fresh Fruit} 0.01158790 0.3203925  1.642617
[6]  {Sauces}            => {Fresh Fruit} 0.01228224 0.3932806  2.016306
[7]  {Tools}             => {Fresh Fruit} 0.01092441 0.3033419  1.555200
[8]  {Pasta}             => {Fresh Fruit} 0.02163280 0.3554767  1.822489
[9]  {Bologna}           => {Fresh Fruit} 0.01041522 0.2085909  1.069422
[10] {TV Dinner}         => {Fresh Fruit} 0.01604715 0.3209877  1.645668
[11] {Conditioner}       => {Fresh Fruit} 0.01526023 0.5079610  2.604259
[12] {Mouthwash}         => {Fresh Fruit} 0.01632489 0.3866959  1.982547
[13] {Coffee}            => {Fresh Fruit} 0.01444244 0.2355310  1.207541
[14] {Shrimp}            => {Fresh Fruit} 0.01077011 0.3541350  1.815611
[15] {Lightbulbs}        => {Fresh Fruit} 0.01853138 0.2870459  1.471652
[16] {Peanut Butter}     => {Fresh Fruit} 0.01317718 0.2475362  1.269091
[17] {Cleaners}          => {Fresh Fruit} 0.01785246 0.3346833  1.715884
[18] {Cooking Oil}       => {Fresh Fruit} 0.01502878 0.2088336  1.070667
[19] {Yogurt}            => {Fresh Fruit} 0.01706553 0.3645353  1.868932
[20] {Muffins}           => {Fresh Fruit} 0.01629403 0.2158626  1.106704

Results/Findings: 1.) Fresh Fruit and fresh vegetables are also positively correlated and purchased with people who buy these two items also buy items like pasta, rice,juice cheese. Items on the LHS Rhs support Confidence Lift {Fresh Fruit,Fresh Vegetables,Pasta} => {Rice} 0.01047710 0.6935649 11.629638 {Fresh Fruit,Fresh Vegetables,Rice} => {Pasta} 0.01047710 0.5843373 9.601860

#subrule for both Fresh Fruit and Fresh Vegetable on the lhs
FreshRules2 <- subset(rules, subset = lhs %ain% c("Fresh Fruit", "Fresh Vegetables"))
summary(FreshRules2)

set of 7 rules

rule length distribution (lhs + rhs):sizes
3 4 
5 2 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  3.000   3.000   3.000   3.286   3.500   4.000 

summary of quality measures:
    support          confidence          lift       
 Min.   :0.01048   Min.   :0.2048   Min.   : 1.506  
 1st Qu.:0.01277   1st Qu.:0.2068   1st Qu.: 1.953  
 Median :0.01511   Median :0.2180   Median : 3.375  
 Mean   :0.01434   Mean   :0.3369   Mean   : 4.873  
 3rd Qu.:0.01567   3rd Qu.:0.4141   3rd Qu.: 6.845  
 Max.   :0.01793   Max.   :0.6936   Max.   :11.630  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

inspect(FreshRules2)

    lhs                                     rhs      support    confidence lift     
[1] {Fresh Fruit,Fresh Vegetables}       => {Pasta}  0.01510593 0.2054133   3.375414
[2] {Fresh Fruit,Fresh Vegetables}       => {Wine}   0.01530652 0.2081410   2.031538
[3] {Fresh Fruit,Fresh Vegetables}       => {Rice}   0.01792961 0.2438103   4.088254
[4] {Fresh Fruit,Fresh Vegetables}       => {Juice}  0.01505964 0.2047839   1.874818
[5] {Fresh Fruit,Fresh Vegetables}       => {Cheese} 0.01603172 0.2180025   1.506239
[6] {Fresh Fruit,Fresh Vegetables,Pasta} => {Rice}   0.01047694 0.6935649  11.629818
[7] {Fresh Fruit,Fresh Vegetables,Rice}  => {Pasta}  0.01047694 0.5843373   9.602008

2.) Canned fruit are not a frequent item and buyers sometimes buy them with fresh vegetables but chances are very less. Sub Rules created for fresh vegetable and canned vegetable on the lhs resulted in 203 itemset having canned vegetables and fresh vegetables together with deli meats ,shrimp, rice and pasta.

#Subrule for fresh Vegetable and Canned Vegetables on lhs.
cannedRules <- subset(rules, subset = lhs %ain% c("Fresh Vegetables", "Canned Vegetables"))
summary(cannedRules)

set of 203 rules

rule length distribution (lhs + rhs):sizes
  3   4 
 21 182 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  3.000   4.000   4.000   3.897   4.000   4.000 

summary of quality measures:
    support          confidence          lift       
 Min.   :0.01021   Min.   :0.2571   Min.   : 1.836  
 1st Qu.:0.01095   1st Qu.:0.7353   1st Qu.: 7.094  
 Median :0.01111   Median :0.7533   Median :10.252  
 Mean   :0.01134   Mean   :0.7122   Mean   :10.160  
 3rd Qu.:0.01128   3rd Qu.:0.7705   3rd Qu.:12.981  
 Max.   :0.01649   Max.   :0.8193   Max.   :19.019  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

inspect(head(cannedRules))

    lhs                                     rhs             support    confidence lift    
[1] {Canned Vegetables,Fresh Vegetables} => {Shrimp}        0.01027635 0.2586408  8.504439
[2] {Canned Vegetables,Fresh Vegetables} => {Peanut Butter} 0.01095527 0.2757282  5.179613
[3] {Canned Vegetables,Fresh Vegetables} => {Sour Cream}    0.01451959 0.3654369  7.704489
[4] {Canned Vegetables,Fresh Vegetables} => {Shampoo}       0.01021463 0.2570874  4.228826
[5] {Canned Vegetables,Fresh Vegetables} => {Rice}          0.01425728 0.3588350  6.017008
[6] {Canned Vegetables,Fresh Vegetables} => {Deli Meats}    0.01063124 0.2675728  3.576227

#visualization for 2nd question
#plotting first 20 subrules with high lift for fresh vegetables on rhs
subrules2 <- head(sort(FreshRules, by="lift"), 20)
plot(subrules2, method="graph")

#plotting subrule for fresh fruit on rhs 
plot(FreshRules1,method="graph",interactive=FALSE,shading=NA)

#plotting subrule for fresh fruit and fresh vegetables on lhs
#plot(FreshRules2,method="graph",interactive=False,shading=NA)
#Plot for comparision of fresh vegetables and canned vegetables
subrules3 <- head(sort(cannedRules, by="lift"), 10)
plot(subrules3,method="graph",interactive=FALSE,shading=NA)

3.) Fresh fruits and fresh vegetables have a strong positive correlation and people buy them very frequently with pasta and rice. 4.) Canned vegetables and fresh vegetables are positively correlated. People buy these mostly with those items that are used for cooking meals for dinner and lunch e: g oil, pasta, rice, cheese, jelly, sour cream and wine. 5.) Canned fruits are not purchased frequently and its sale is independent of fresh fruits.

3.) Small vs large transactions

# 3. Small and Large transaction
#Subrule for small baskets with item less than or equal to 2
rulesSmallSize <- subset(rules, subset = size(rules) <=2 )
#summary for ruleSmallSize
summary(rulesSmallSize)

set of 787 rules

rule length distribution (lhs + rhs):sizes
  1   2 
  1 786 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   2.000   2.000   1.999   2.000   2.000 

summary of quality measures:
    support          confidence          lift        
 Min.   :0.01001   Min.   :0.2001   Min.   : 0.7122  
 1st Qu.:0.01235   1st Qu.:0.2341   1st Qu.: 2.2477  
 Median :0.01575   Median :0.2775   Median : 3.1529  
 Mean   :0.01782   Mean   :0.3033   Mean   : 3.6580  
 3rd Qu.:0.02092   3rd Qu.:0.3527   3rd Qu.: 4.7097  
 Max.   :0.30861   Max.   :0.7080   Max.   :15.5760  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

inspect(head(rulesSmallSize))

    lhs                   rhs                support    confidence lift     
[1] {}                 => {Fresh Vegetables} 0.30861454 0.3086145  1.0000000
[2] {Canned Fruit}     => {Fresh Vegetables} 0.01418013 0.4240886  1.3741692
[3] {Deli Salads}      => {Fresh Vegetables} 0.01220509 0.2878457  0.9327030
[4] {Personal Hygiene} => {Fresh Vegetables} 0.01692666 0.3269747  1.0594921
[5] {Plastic Utensils} => {Fresh Vegetables} 0.01127930 0.2515485  0.8150896
[6] {Spices}           => {Wine}             0.01015291 0.2222973  2.1697087

In the transaction dataset finding a small baskets having less than or equal to 2 items with frequent itemset were found to be 787. Few items having strong positive correlation are as follows. {Candles} => {Fresh Chicken} 0.01035366 0.4059286 15.5757381 {Fresh Chicken} => {Candles} 0.01035366 0.3972765 15.5757381 {Candles} => {Sauces} 0.01027651 0.4029038 12.9008845 {Sauces} => {Candles} 0.01027651 0.3290514 12.9008845

Some items that are negatively correlated are :

{French Fries} => {Fresh Vegetables} 0.01151092 0.2197996 0.7122032 {Donuts} => {Fresh Vegetables} 0.01265276 0.2388581 0.7739572

Results/ Findings : 1.) This reflects that people who purchase unhealthy and sugary food rarely buy fresh vegetables. Fresh vegetables are mostly purchased with sauces, candle and fresh chicken. Discussed in previous part.

#Subrule for Large baskets with item more than or equal to 5
rulesLargeSize <- subset(rules, subset = size(rules) >= 5 )
summary(rulesLargeSize)

set of 400 rules

rule length distribution (lhs + rhs):sizes
  5 
400 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      5       5       5       5       5       5 

summary of quality measures:
    support          confidence          lift       
 Min.   :0.01001   Min.   :0.6788   Min.   : 2.236  
 1st Qu.:0.01027   1st Qu.:0.7999   1st Qu.: 7.634  
 Median :0.01054   Median :0.8173   Median : 8.375  
 Mean   :0.01063   Mean   :0.8162   Mean   : 9.841  
 3rd Qu.:0.01083   3rd Qu.:0.8345   3rd Qu.:12.220  
 Max.   :0.01258   Max.   :0.8884   Max.   :19.659  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

#inspect(rulesLargeSize)
inspect(head(sort(rulesLargeSize, by ="lift"),5))

    lhs                   rhs              support confidence     lift
[1] {Cottage Cheese,                                                  
     Fresh Vegetables,                                                
     Frozen Chicken,                                                  
     Sliced Bread}     => {Deodorizers} 0.01038436  0.8147700 19.65913
[2] {Fresh Vegetables,                                                
     Frozen Chicken,                                                  
     Juice,                                                           
     Sliced Bread}     => {Deodorizers} 0.01058495  0.8108747 19.56514
[3] {Fresh Vegetables,                                                
     Frozen Chicken,                                                  
     Pancake Mix,                                                     
     Sliced Bread}     => {Deodorizers} 0.01019920  0.8100490 19.54522
[4] {Cereal,                                                          
     Fresh Vegetables,                                                
     Frozen Chicken,                                                  
     Sliced Bread}     => {Deodorizers} 0.01036893  0.8076923 19.48836
[5] {Frozen Chicken,                                                  
     Juice,                                                           
     Pancake Mix,                                                     
     Sliced Bread}     => {Deodorizers} 0.01018377  0.8068460 19.46794

2.) Itemset having more than or equal to 5 items in a basket are found to be 400.When a customer buy 5 or more items are found to have a positive correlation.

# Visualization for question 3 
#plotting rulesSmallSize for small item basket
plot(rulesSmallSize, method="paracoord")

number of rows of result is not a multiple of vector length (arg 2)

# Interactive plot for rulesSmallSize
#sel <- plot(rulesSmallSize, measure=c("support", "lift"), shading="confidence", interactive=TRUE)
# plotting large itemset
plot(rulesLargeSize, method="paracoord")

#Interactice plot rulesLargeSize
#sel <- plot(rulesLargeSize, measure=c("support", "lift"), shading="confidence", interactive=TRUE)

3.) Large Itemset mostly contain items that are used to cook full meals, dinner and breakfast. Fresh vegetables, fresh chicken, juice and sliced bread are found to be positively correlated with deodorizer.

4.) Dairy (milk) Vs cereals.

# 4.One more intresting pattern:Milk and Cereal
#  Subsets. find subset of rules that has Milk on the Rhs and Cereal on lhs
Rulesinterest1 <- subset(rules, subset = rhs %pin%  "Milk" & lhs %ain% "Cereal")
#Summary of Rulesinterest1
summary(Rulesinterest1)

set of 24 rules

rule length distribution (lhs + rhs):sizes
 2  3  4  5 
 1  7 15  1 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   3.000   4.000   3.667   4.000   5.000 

summary of quality measures:
    support          confidence          lift      
 Min.   :0.01003   Min.   :0.2190   Min.   :2.451  
 1st Qu.:0.01141   1st Qu.:0.5485   1st Qu.:6.139  
 Median :0.01152   Median :0.6173   Median :6.910  
 Mean   :0.01234   Mean   :0.5899   Mean   :6.603  
 3rd Qu.:0.01359   3rd Qu.:0.6768   3rd Qu.:7.576  
 Max.   :0.01961   Max.   :0.7088   Max.   :7.934  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

inspect(Rulesinterest1)

     lhs                                     rhs    support    confidence lift    
[1]  {Cereal}                             => {Milk} 0.01961147 0.2189869  2.451178
[2]  {Cereal,Cottage Cheese}              => {Milk} 0.01365551 0.5466337  6.118616
[3]  {Cereal,Jam}                         => {Milk} 0.01394868 0.5854922  6.553569
[4]  {Cereal,Jelly}                       => {Milk} 0.01371723 0.5746606  6.432328
[5]  {Cereal,Waffles}                     => {Milk} 0.01356293 0.5369578  6.010311
[6]  {Cereal,Sliced Bread}                => {Milk} 0.01407212 0.4532803  5.073686
[7]  {Cereal,Juice}                       => {Milk} 0.01396411 0.4408183  4.934196
[8]  {Cereal,Fresh Vegetables}            => {Milk} 0.01138731 0.3152499  3.528675
[9]  {Cereal,Cottage Cheese,Jam}          => {Milk} 0.01146446 0.6956929  7.787074
[10] {Cereal,Cottage Cheese,Jelly}        => {Milk} 0.01126387 0.6932574  7.759813
[11] {Cereal,Cottage Cheese,Waffles}      => {Milk} 0.01120215 0.6836158  7.651893
[12] {Cereal,Cottage Cheese,Sliced Bread} => {Milk} 0.01155704 0.6035455  6.755645
[13] {Cereal,Cottage Cheese,Juice}        => {Milk} 0.01158790 0.6100731  6.828710
[14] {Cereal,Jam,Jelly}                   => {Milk} 0.01144903 0.6745455  7.550366
[15] {Cereal,Jam,Waffles}                 => {Milk} 0.01147989 0.6901670  7.725221
[16] {Cereal,Jam,Sliced Bread}            => {Milk} 0.01177306 0.6758193  7.564624
[17] {Cereal,Jam,Juice}                   => {Milk} 0.01181935 0.6666667  7.462176
[18] {Cereal,Jelly,Waffles}               => {Milk} 0.01114043 0.6798493  7.609733
[19] {Cereal,Jelly,Sliced Bread}          => {Milk} 0.01141817 0.6654676  7.448755
[20] {Cereal,Jelly,Juice}                 => {Milk} 0.01147989 0.6549296  7.330800
[21] {Cereal,Sliced Bread,Waffles}        => {Milk} 0.01140274 0.6158333  6.893185
[22] {Cereal,Juice,Waffles}               => {Milk} 0.01144903 0.6188490  6.926941
[23] {Cereal,Juice,Sliced Bread}          => {Milk} 0.01174220 0.5490620  6.145797
[24] {Cereal,Jam,Juice,Sliced Bread}      => {Milk} 0.01002947 0.7088332  7.934157

Milk is one of the most frequent item in the item sets .Finding patterns of one more item that is very frequent with milk is cereals.Analysing 24 itemset having milk on the rhs and cereals on the left hand side it is found that both the item are positively correlated .Buyers who buy cereals with jelly jam sliced bread also buy milk and vice versa.

#Subsets. find subset of rules that has Milk on the lhs and Cereal on rhs
Rulesinterest2 <- subset(rules, subset = lhs %ain%  "Milk" & rhs %ain% "Cereal")
summary(Rulesinterest2)

set of 24 rules

rule length distribution (lhs + rhs):sizes
 2  3  4  5 
 1  7 15  1 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   3.000   4.000   3.667   4.000   5.000 

summary of quality measures:
    support          confidence          lift      
 Min.   :0.01003   Min.   :0.2195   Min.   :2.451  
 1st Qu.:0.01141   1st Qu.:0.6986   1st Qu.:7.801  
 Median :0.01152   Median :0.8246   Median :9.208  
 Mean   :0.01234   Mean   :0.7369   Mean   :8.228  
 3rd Qu.:0.01359   3rd Qu.:0.8365   3rd Qu.:9.340  
 Max.   :0.01961   Max.   :0.8519   Max.   :9.513  

mining info:
         data ntransactions support confidence
 transactions         64809    0.01        0.2

inspect(Rulesinterest2)

     lhs                                   rhs      support    confidence lift    
[1]  {Milk}                             => {Cereal} 0.01961147 0.2195164  2.451178
[2]  {Cottage Cheese,Milk}              => {Cereal} 0.01365551 0.7577055  8.460740
[3]  {Jam,Milk}                         => {Cereal} 0.01394868 0.7062500  7.886174
[4]  {Jelly,Milk}                       => {Cereal} 0.01371723 0.7186742  8.024906
[5]  {Milk,Waffles}                     => {Cereal} 0.01356293 0.6756341  7.544309
[6]  {Milk,Sliced Bread}                => {Cereal} 0.01407212 0.5595092  6.247628
[7]  {Juice,Milk}                       => {Cereal} 0.01396411 0.5441972  6.076650
[8]  {Fresh Vegetables,Milk}            => {Cereal} 0.01138731 0.3744292  4.180976
[9]  {Cottage Cheese,Jam,Milk}          => {Cereal} 0.01146446 0.8320269  9.290632
[10] {Cottage Cheese,Jelly,Milk}        => {Cereal} 0.01126387 0.8381171  9.358637
[11] {Cottage Cheese,Milk,Waffles}      => {Cereal} 0.01120215 0.8268793  9.233153
[12] {Cottage Cheese,Milk,Sliced Bread} => {Cereal} 0.01155704 0.8359375  9.334299
[13] {Cottage Cheese,Juice,Milk}        => {Cereal} 0.01158790 0.8400447  9.380162
[14] {Jam,Jelly,Milk}                   => {Cereal} 0.01144903 0.8318386  9.288530
[15] {Jam,Milk,Waffles}                 => {Cereal} 0.01147989 0.8175824  9.129342
[16] {Jam,Milk,Sliced Bread}            => {Cereal} 0.01177306 0.8293478  9.260717
[17] {Jam,Juice,Milk}                   => {Cereal} 0.01181935 0.8426843  9.409636
[18] {Jelly,Milk,Waffles}               => {Cereal} 0.01114043 0.8223235  9.182281
[19] {Jelly,Milk,Sliced Bread}          => {Cereal} 0.01141817 0.8390023  9.368521
[20] {Jelly,Juice,Milk}                 => {Cereal} 0.01147989 0.8406780  9.387233
[21] {Milk,Sliced Bread,Waffles}        => {Cereal} 0.01140274 0.8211111  9.168744
[22] {Juice,Milk,Waffles}               => {Cereal} 0.01144903 0.8281250  9.247063
[23] {Juice,Milk,Sliced Bread}          => {Cereal} 0.01174220 0.6320598  7.057747
[24] {Jam,Juice,Milk,Sliced Bread}      => {Cereal} 0.01002947 0.8519004  9.512545

#Visualization for question 4;
#Plot for Rulesinterest1 that has Milk on the rhs and cereal on the lhs
plot(Rulesinterest1, method="paracoord")

#Plot for Rulesinterest2 that has milk on the lhs and cereal on the rhs
plot(Rulesinterest2, method="graph")

Results/ Findings: 1.) People who buy cereal are very likely to buy milk. It is supported by more than 80 % confidence level. 2.) Buyers who buy milk also likely to buy cereal. 3.) Cereal and milk are positively correlated and mostly purchased together with other items that are used in making breakfast. Recommendations: Based on the findings the output of the analysis reflects how frequently items co-occur in transactions. This is a function both of the strength of association between the items, and the way the FDMart owner has presented them in different aisles. The closely related item might reoccur several times not because they are “naturally” connected, but there is a chance because the way they are placed in a shelve is motivating people to buy these items together. Item pairs that are frequently selling together should be placed close together within broader categories. Like for example our data tells that wine and candles are sold very often together. Since good wines are costly and bring high profits to business, it can be placed next to fragrant candles. In this way grocery owner can couple most popular item like candle with items that has high margin like wine. In addition , grocery store can offer discount coupons for the items that are frequently bundled together like beer and gums .Giving some discounts and placing these two item next to each other will motivate those buyers to buy beer ,who just visited shop to purchase gums. This will drive significant uplift in profit. Mostly baskets have 5 to 6 items in a itemset. Coupling high price items with low price products can make a significant increase in total number of items purchased in a single transaction. Moreover, Items that are very likely to be sold together for example milk and cereal can be couple with sliced bread. Since milk and cereal goes very frequently and milk also goes with sliced bread also. We can connect bread and cereal in order to increase sale of bread. There are so many possibilities as you go on with the analysis with data mining.